Sylvie and Bruno Economics

I have been flipping through a new popular book by the physicist turned economist J Doyne Farmer. It is entitled Making Sense of Chaos (2024) and carries the subtitle 'A better Economics for a Better World'. Farmer's thesis is fairly simple. He starts by distinguishing two separate approaches to modelling economic phenomena - the first he labels 'standard economic theory' and summarises thus;​

'In standard macroeconomic models, households get utility from consumption and firms get utility from making profits while minimizing risk. Under standard economic theory, each agent makes decisions that make her own utility as large as possible. To find these decisions and understand their economic consequences, economists write down and solve equations'

 J Doyne Farmer, Making Sense of Chaos (Penguin Books: 2024) 

This is perhaps a caricature but is a fairly good one insofar as it captures the main outlines of how economics is usually done today. The second approach, which Farmer champions in the book, is that of 'complexity economics' which is built on the central dogma of 'complexity science' -  that large complex systems exhibit behaviour that is 'qualitatively different' from their component parts. Using the more homely language of the legendary physicist Philip W Anderson, more is not always more, sometimes 'more is different'. Under this central dogma we can jettison most of the elements of the 'standard theory' - no rationality, certainly no representative agents or households or firms, and (in most cases) no stable equilibria. Naturally, we also have to exchange tools. Out goes the DSGE with its stack of linear equations, in comes a new 'workhorse', the agent-based model. From this point onwards we will do our economics the way we do other science, via computer simulation. After all if we can create simulations of 'galaxy formation, protein folding, the brain, epidemics, battle tactics and traffic jams', why not just build a 'fine-grained' model of the whole economy and simulate its behaviour?

It's a very attractive idea, though it is not all that new. The complexity economics movement is only a little younger than Farmer himself, who now in his 72nd year sports an impressive beard that makes him look like a latter-day John Ruskin. In the time since Farmer helped organise the original complexity economics conferences in Santa Fe in the 1980s, there has been minimal uptake of these ideas (though this seems to be changing). Part of the argument of the book is that the reason complexity economics failed to make a breakthrough is because its techniques required greater computational resources than those that were available when the movement first constituted itself. However, the inexorability of Moore's law has, so it would seem, carried away the obstacles that had previously hemmed in the complexity revolution, which is now in a position to dislodge the old orthodoxy of the standard economic model.

Reflecting on the opening section of Farmer's book, there is another obstacle that the complexity school has to consider. I will call it the “Sylvie and Bruno Paradox” after the great fairy-tale by Lewis Carroll. In volume II of that novel the eponymous characters, the fairies Sylvie and Bruno, find themselves in discussion with an extra-terrestrial traveller known as 'Mein Herr'. We discover that the denizens of Mein Herr's planet, among other strange practices, developed an obsession with map making that had driven them to make bigger and bigger maps until they reached a unique map with a one-to-one scale:

"What a useful thing a pocket-map is!" I remarked.

"That's another thing we've learned from your Nation," said Mein Herr, "map-making. But we've carried it much further than you. What do you consider the largest map that would be really useful?"

"About six inches to the mile."

"Only six inches!" exclaimed Mein Herr. "We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all ! We actually made a map of the country, on the scale of a mile to the mile!"

"Have you used it much?" I enquired.​

"It has never been spread out, yet," said Mein Herr: "the farmers objected: they said it would cover the whole country, and shut out the sunlight ! So we now use the country itself, as its own map, and I assure you it does nearly as well."

Lewis Carrol, Sylvie and Bruno Concluded, MacMillan & Co, London: 1894), p. 169

The analogy, I trust, is obvious. As with Mein Herr the complexity economist wants to explain his chosen object by representing it in a way that preserves that object's specific complexity. And so he must make a complex model. The difficulty arises in trying to find a non-arbitrary threshold for the amount of complexity that goes into the model, all while battling the two statistical devils of 'initial conditions' and 'degrees of freedom'. ​​

Farmer is obviously aware of this, invoking what he calls the 'principle of verisimilitude - 'that good models should be as simple as possible, but no simpler' -  as a way to get out of Mein Herr’s mad logical spiral. I had assumed this was a reference to Karl Popper's paper 'Some Comments on Truth and the Growth of Knowledge' (1962), where the notion of 'verisimilitude' as a measure of the closeness to truth of an otherwise false theory was first given its basic philosophical statement. However I can't find any mention of Popper in the book. A nice summary of the problem of verisimilitude is given by the logician Pavel Tichy, who was also responsible for showing up a number of errors in Popper's own theories about truth-likeness:

The problem of truthlikeness (verisimilitude, nearness to the truth) has been  described as one of the most fundamental problems in philosophy of science.  The scientist is not someone who knows the truth. Rather, he traffics in falsehoods: what he has to offer are conjectural theories which represent better or worse approximations to the truth. Thus when we judge one theory superior to another we cannot mean simply that while the latter theory is  false the former is true. For, more likely than not, the superior theory will also be false. What we mean is rather that the better theory is one which is closer to the truth, which diverges from the truth less than the other theory does.​

There seem absolutely obvious cases of one statement's being nearer to the  truth than another. The man who maintains that there are exactly eight planets in the Solar System is undeniably closer to the truth than his opponent who insists that there are only five. It is not immediately obvious, however, how to abstract from such intuitively indisputable cases a definition which would state in general terms precisely what it takes for an arbitrary sentence to be closer to the truth than another sentence of the same language.

​​P Tichy, 'Verisimilitude Revisisted' in Synthese, Vol. 38, No. 2, Verisimilitude (Jun., 1978), pp. 175-196

As ever the constraints of the blog-form bite at this point, and in the nick of time as well, as I don't have a great deal of light to shed on this devilishly difficult problem. All I will say is that the example Tichy gives here of an ‘obvious’ case of two statements with different degrees of truthlikeness shows up the difficulty of creating a logical theory of verisimilitude that could extend to models of complex systems where thousands of interactions between heterogeneous agents need to be represented.

My own view, for what it is worth (not much really!), is that complexity economics is full of promise, and that the broad itinerary for economic reform outlined by Farmer needs trying, even if only for lack of other options. However, I suspect that it will not yield the same order of precise prediction that we get in, to use Farmer's example, the dynamics of galaxies. What it may be able to do is provide, to adapt a phrase from the literary critic I A Richards, a 'speculative instrument' - a means of looking not into the future, but into possible worlds. So long as we do not mistake possible worlds for the future, that will be a huge contribution.

Photo by pure julia on Unsplash

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